For myself, I've always used extra defenses and KB protection to simulate invulnerability.

The main reason is because that's the way it's done in the source material. The word invulnerable is misused to describe characters because it's cooler that just saying the character is just exceptionally tough.

Let's take our classic example, Superman. He's immune to pretty much all conventional weapons and most unusual ones. For the most part, his villains tend to distract and divert him or use his weaknesses against him. But throughout his history, he's had foes that can go toe to toe with him such as Bizarro, Darkseid, Mongul and Doomsday. None of these villains use tricks, they just do enough damage to get through Superman's defenses. If their attacks were to get in a square blow against the lesser JLA'ers such as Batman or Green Arrow the results would be ......unfortunate.

So when someone says they want their character to be "Invulnerable", I look at their defenses and give them a number that would effective allow them to take 95% of the campaign villains attacks with little to negligible damage. Usually I'll only allow this against a special effect but I've allowed it on physical or energy attacks in general with the caveat of a fairly known weakness or vulnerability to something attached to the character. The player has got to trust me when I tell him that only a world beating threat or an agreed upon nemesis will breach his defenses and I as the GM have to be worthy of that trust.

IMO shape change only changes your shape. At the basic level, you don't turn into a fly; you become fly-shaped. Shrinking may allow you to become fly-sized and flight may allow you to fly, but you still don't look like an actual fly.in fact, the difference between you and an actual fly is a Special Effect unique enough to identify that it is actually you. E.g. Beast boy can change his shape and size into any animal, but they are all a very distinctive shade of green.

IMO shape change only changes your shape. At the basic level, you don't turn into a fly; you become fly-shaped. Shrinking may allow you to become fly-sized and flight may allow you to fly, but you still don't look like an actual fly.in fact, the difference between you and an actual fly is a Special Effect unique enough to identify that it is actually you. E.g. Beast boy can change his shape and size into any animal, but they are all a very distinctive shade of green.